Congressional Republicans said Thursday that they would introduce legislation to wind down Fannie Mae and Freddie Mac over five years and cede the companies' roles to the private mortgage market, which has remained mostly dormant since melting down six years ago.

The bill would create a new utility-like platform for investors to securitize mortgages without a government guarantee, while repealing new curbs on the mortgage-bond market in the Dodd-Frank financial-overhaul bill. It also proposes restricting access to loans...